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Journal of Physics Condensed Matter

The stepped spin - Peierls phase transition in the quasi-one-dimensional spin-1/2 quantum XY-model

Yanjiang Ji, Jun Qi, Jian‐Xin Li, Chang-De Gong

Published Mar 10, 1997• 4 citations
Publisher

Abstract

Using an extension of the Jordan - Wigner transformation (JWT) in two dimensions, the effects of weak interchain coupling on the spin - Peierls (SP) system is studied. The magnetic interaction is considered to be a quantum XY-interaction, and the spin - lattice distortion is treated quasiclassically. On the analogy of the stepped Peierls transition theory, we propose a stepped SP transition theory. We find that, when any finite transverse coupling is introduced between nearest chains, the usual SP transition will be modified, and the dimerization and the opening of the gap will no longer occur simultaneously. This leads to the appearance of a gapless SP phase over a certain temperature region.

DOI
10.1088/0953-8984/9/10/013

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Using an extension of the Jordan - Wigner transformation (JWT) in two dimensions, the effects of weak interchain coupling on the spin - Peierls (SP) system is studied. The magnetic interaction is considered to be a quantum XY-interaction, and the spin - lattice distortion is treated quasiclassically. On the analogy of the stepped Peierls transition theory, we propose a stepped SP transition theory. We find that, when any finite transverse coupling is introduced between nearest chains, the usual SP transition will be modified, and the dimerization and the opening of the gap will no longer occur simultaneously. This leads to the appearance of a gapless SP phase over a certain temperature region.
The two-dimensional Jordan-Wigner transformation is used to investigate the zero-temperature spin-Peierls transition for an anisotropic two-dimensional XY\mathrm{XY}XY model in the adiabatic limit. The phase diagram between the dimerized (D) state and uniform (U) state is shown in the parameter space of dimensionless interchain coupling $h{(=J}_{\ensuremath{\perp}}/J)$ and spin-lattice coupling \ensuremath{\eta}. It is found that the spin-lattice coupling $\ensuremath{\eta}$ must exceed some critical value ${\ensuremath{\eta}}_{c}$ in order to reach the D phase for any finite h. The dependence of ${\ensuremath{\eta}}_{c}$ on h is given by $\ensuremath{-}1/\mathrm{ln}h$ for $\stackrel{\ensuremath{\rightarrow}}{h}0$ and the transition between the U and D phases is of first order for at least $h>{10}^{\ensuremath{-}3}.$
The zero and finite temperature spin-Peierls transitions in a quasi-one-dimensional spin-12\frac{1}{2}21​ Heisenberg model coupled to adiabatic bond phonons is investigated using the stochastic series expansion (SSE) quantum Monte Carlo (QMC) method. The quantum phase transition from a gapless N\'eel state to a spin-gapped Peierls state is studied in the parameter space spanned by spatial anisotropy, interchain coupling strength, and spin-lattice coupling strength. It is found that for any finite interchain coupling, the transition to a dimerized Peierls ground state only occurs when the spin-lattice coupling exceeds a finite, nonzero critical value. This is in contrast to the pure 1D model (zero interchain coupling), where adiabatic/classical phonons lead to a dimerized ground state for any nonzero spin-phonon interaction. The phase diagram in the parameter space shows that for a strong interchain coupling, the relation between the interchain coupling and the critical value of the spin-phonon interaction is linear whereas for weak interchain coupling, this behavior is found to have a natural logarithmlike relation. No region was found to have a long range magnetic order and dimerization occurring simultaneously. Instead, the N\'eel state order vanishes simultaneously with the setting in of the spin-Peierls state. For the thermal phase transition, a continuous heat capacity with a peak at the critical temperature Tc{T}_{c}Tc​ shows a second order phase transition. The variation of the equilibrium bond length distortion ${\ensuremath{\delta}}_{eq}$ with temperature showed a power law relation which decayed to zero as the temperature was increased to Tc{T}_{c}Tc​, indicating a continuous transition from the dimerized phase to a paramagnetic phase with uniform bond length and zero antiferromagnetic susceptibility.
The model that we study is a two-XY-quantum-spin-chain system with Ising interchain magnetic interaction. This model, referred to as the spin-ladder model, is used as a first step to model the thermodynamic properties of low-dimensional spin system. Similarities between the spin-ladder model and the one-dimensional Hubbard model are used in our analysis. As a consequence we can qualitatively understand the heat capacity and spin susceptibilty and show that both measurements are necessary to analyze a spin-ladder system. We also show that the strong-interchain-coupling limit of the spin-ladder model is equivalent to a one-chain spin Heisenberg Hamiltonian. Furthermore, the spin-Peierls transition is investigated for small (\ensuremath{\Vert}I/2J\ensuremath{\Vert}\ensuremath{\ll}1) and large (\ensuremath{\Vert}I/2J\ensuremath{\Vert}\ensuremath{\gg}1) interchain coupling, and we show its occurrence at relatively small spin-phonon coupling (\ensuremath{\lambda}\ensuremath{\lesssim}0.6). From the results obtained for the small- and large-interchain-interaction limits, we propose the conjecture that the in-phase dimerization persists for all values of the interaction parameter at zero temperature.
We study the spin-Peierls (SP) transition of one-dimensional chain polymeric complexes coupled to lattice by means of many-body Green's function theory. The chain effective elastic constant is an intrinsic factor that determines the order of SP transition. It is found that the SP transition temperature T(SP) and the susceptibility-maximum temperature T(max) are in agreement with the experimental results. When an external magnetic field is applied to the chain, it makes T(SP) and T(max) decrease, and drives the SP transition from the second order to the first order. Besides, we show that the two-site thermal entanglement entropy is a good indicator of SP transition. Further considering the effect of interchain coupling on SP transition, with weak coupling of double-chain, the theoretical values are closer to the experimental results. We also calculate the density of states and spectral functions, which show that the energy gap vanishes at a critical temperature lower than T(SP), indicating a gapless SP phase lies in the gapped dimerized phase. The interchain coupling can drive the SP transition from the second order to the first order, while the SP dimerization may collapse for large interchain couplings.
The spin-Peierls transition in the ground state of a quasi-one-dimensional spin-1/2 Heisenberg model coupled to adiabatic bond phonons is studied using a quantum Monte Carlo (QMC) method. The transition from a gapless Neel state to a spin-gapped Peierls state is explored in the parameter space spanned by the spatial anisotropy and the strength of spin-lattice coupling. It is found that for any finite inter-chain coupling, the transition to a dimerized Peierls ground state occurs only when the spin-lattice coupling exceeds a finite, non-zero critical value. This is in contrast to the pure 1D model, where adiabatic phonons lead to a dimerized ground state for any non-zero spin-phonon coupling. The phase diagram in the above parameter space is mapped out. No evidence is found for a region of co-existing long range magnetic order and dimerization. The vanishing of the Neel order occurs simultaneously with the setting in of the dimerization.
The spin–Peierls phase transition in a quasi-one-dimensional XY chain of S=1/2 of spins interacting through an anisotropic exchange interaction is studied as a function of the degree of anisotropy γ. The spin–Peierls state is described using a mean field theory. As γ increases (small value of the anisotropy), the transition temperature Tc decreases. For intermediate values of the anisotropy parameter γ, a tricritical point separating the regions of first and second order phase transitions is obtained. For larger values of γ, a total suppression of the spin–Peierls state is predicted. Finally, a very unusual temperature dependent gap of the elementary spin excitations is predicted for the anisotropic XY system.